Completely Pseudo-valuation Rings and Their Extensions
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 249
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Recall that a commutative ring $R$ is said to be a pseudo-valuation ring if every prime ideal of $R$ is strongly prime. We define a completely pseudo-valuation ring. Let $R$ be a ring (not necessarily commutative). We say that $R$ is a completely pseudo-valuation ring if every prime ideal of $R$ is completely prime. With this we prove that if $R$ is a commutative Noetherian ring, which is also an algebra over $\mathbb{Q}$ (the field of rational numbers) and $\delta$ a derivation of $R$, then $R$ is a completely pseudo-valuation ring implies that $R[x;\delta]$ is a completely pseudo-valuation ring. We prove a similar result when prime is replaced by minimal prime.
Classification :
16S36 16N40 16P40
@article{PIM_2014_N_S_95_109_a19,
author = {Vijay Kumar Bhat},
title = {Completely {Pseudo-valuation} {Rings} and {Their} {Extensions}},
journal = {Publications de l'Institut Math\'ematique},
pages = {249 },
publisher = {mathdoc},
volume = {_N_S_95},
number = {109},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a19/}
}
Vijay Kumar Bhat. Completely Pseudo-valuation Rings and Their Extensions. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 249 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a19/